First anime dvd was Cowboy Bebop volume one. In fact the reason I bought a dvd player was for anime, right now I only have two non-anime dvds.
First anime I ever bought was Gunsmith Cats 01 on VHS. All it contained was episode one, which was quite a rip-off now that I start thinking about it. I had just found out about anime and had been browsing some magazine when I saw an ad for the show. When I hit a comic book store downtown and recognized it I decided to give it a shot.